Deep Reinforcement Learning for Concentric Tube Robot Control with a Goal-Based Curriculum

Concentric Tube Robots (CTRs), a type of continuum robot, are a collection of concentric, pre-curved tubes composed of super elastic nickel titanium alloy. CTRs can bend and twist from the interactions between neighboring tubes causing the kinematics and therefore control of the end-effector to be very challenging to model. In this paper, we develop a control scheme for a CTR end-effector in Cartesian space with no prior kinematic model using a deep reinforcement learning (DRL) approach with a goal-based curriculum reward strategy. We explore the use of curricula by changing the goal tolerance through training with constant, linear and exponential decay functions. Also, relative and absolute joint representations as a way of improving training convergence are explored. Quantitative comparisons for combinations of curricula and joint representations are performed and the exponential decay relative approach is used for training a robust policy in a noise-induced simulation environment. Compared to a previous DRL approach, our new method reduces training time and employs a more complex simulation environment. We report mean Cartesian errors of 1.29 mm and a success rate of 0.93 with a relative decay curriculum. In path following, we report mean errors of 1.37 mm in a noise-induced path following task. Albeit in simulation, these results indicate the promise of using DRL in model free control of continuum robots and CTRs in particular.